RESEARCH BASE

Search 3,721 documents across 34 fields — every claim tier-rated by evidence

3,721 Documents 34 Sections 43,625 Citations 34,852 Keywords Indexed 4 Evidence Tiers

3,633 are the core, quality-scored corpus (34 lettered sections — see How We Work); the remaining 88 are cross-corpus synthesis documents (68 InterDocs, 12 Connections, 8 Theories) also indexed here.

9 results for "Hodge conjecture"

V_4_04 Verified Mathematics & Information

V_4_04 — Unsolved Problems in Mathematics

Mathematics has always been driven by problems that resist solution — conjectures so deep that their resolution reshapes entire fields. The Clay Mathematics Institute's seven Millennium Prize Problems ($1 million each, a

unsolved problems Millennium Prize Riemann hypothesis P vs NP Navier-Stokes Hodge conjecture

Q_1_15 Credible Cosmology & Physics

Q_1_15 — Dark Energy Models and Quintessence

The accelerating expansion of the universe, discovered in 1998 via Type Ia supernovae, demands an explanation. The simplest model — Einstein's cosmological constant Λ with equation of state $w = p/\rho = -1$ exactly — fi

dark energy quintessence cosmological constant equation of state w parameter phantom energy

ZA_5_11 Verified Physics & Quantum

ZA_5_11 — Quantum Chaos: Where Classical Chaos Meets Quantum Mechanics

Quantum chaos investigates the quantum-mechanical signatures of systems whose classical counterparts exhibit chaotic behavior — addressing the profound question of how quantum mechanics, which is fundamentally linear, en

quantum chaos random matrix theory level statistics quantum scars stadium billiard Berry conjecture

V_2_16 Verified Mathematics & Information

V_2_16 — Analytic Number Theory

Analytic number theory applies the methods of mathematical analysis — complex analysis, Fourier analysis, probability, and asymptotic estimation — to study the distribution and properties of integers, especially prime nu

analytic number theory Riemann zeta function prime number theorem Dirichlet series L-functions Riemann hypothesis

V_2_09 Verified Mathematics & Information

V_2_09 — Number Theory: Primes, Patterns, and Unsolved Problems

Number theory — the study of integers and their properties — is one of the oldest and most beautiful branches of mathematics, yet it connects to cryptography, physics, and computer science in profound ways. Prime numbers

number theory prime numbers prime distribution Riemann hypothesis Riemann zeta function twin primes

V_2_01 Verified Mathematics & Information

V_2_01 — Prime Numbers — Patterns, Mysteries, and the Riemann Hypothesis

Prime numbers — integers greater than 1 divisible only by 1 and themselves — have fascinated mathematicians since Euclid proved their infinitude (~300 BCE). Despite appearing randomly distributed, primes follow deep stat

prime numbers Riemann hypothesis zeta function Euclid RSA cryptography twin primes

V_2_14 Verified Mathematics & Information

V_2_14 — Differential Topology and Manifolds

Differential topology studies smooth manifolds — spaces that locally resemble Euclidean $\mathbb{R}^n$ with smooth (infinitely differentiable) transition maps — and the smooth maps between them, classified up to diffeomo

differential topology manifold smooth manifold diffeomorphism tangent bundle vector field

V_2_12 Verified Mathematics & Information

V_2_12 — Algebraic Geometry

Algebraic geometry — the study of geometric objects defined by polynomial equations — is one of the most central and technically demanding branches of modern mathematics, connecting algebra, geometry, topology, and numbe

algebraic geometry variety scheme polynomial equation projective space elliptic curve

ZA_2_17 Credible Physics & Quantum

ZA_2_17 — Emergent Spacetime & ER=EPR Conjecture

The ER=EPR conjecture — proposed by Juan Maldacena and Leonard Susskind in 2013 — posits that Einstein-Rosen bridges (wormholes, "ER") and Einstein-Podolsky-Rosen entanglement ("EPR") are fundamentally the same phenomeno

ER=EPR emergent spacetime holographic principle entanglement AdS/CFT quantum gravity

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